# An Etymological Dictionary of Astronomy and AstrophysicsEnglish-French-Persian

## فرهنگ ریشه شناختی اخترشناسی-اخترفیزیک

### M. Heydari-Malayeri    -    Paris Observatory

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Number of Results: 6 Search : orthogonal
 orthogonal   ارداکنج   ardâkonjFr.: orthogonal   In elementary geometry, pertaining to or involving right angles or perpendiculars. Of a system of real functions, defined so that the integral of the product of any two different functions is zero. Of a linear transformation, defined so that the length of a vector under the transformation equals the length of the original vector. Of a square matrix, defined so that its product with its transpose results in the identity matrix.→ ortho- + gonia "angle," related to gony "knee;" L. genu "knee;" Mod.Pers. zânu "knee;" Av. žnav-, žnu- "knee;" Skt. janu-; PIE base *g(e)neu-, see below, + → -alArdâkonj, from ardâ-, → ortho-, + konj "angle, corner, confined place" (variants xong "corner, angle," Tabari kânj, Kurd. kunj, Hamadâni kom), maybe from the PIE base *g(e)neu-, as above, and related to Mod.Pers. zânu "knee" (Av. žnu-), Skt. kona- "angle, corner," Gk. gony, gonia, L. cuneus "a wedge," Albanian (Gheg dialect) kân "angle, corner," Albanian (Toks) kënd "angle, corner." orthogonal functions   کریاهایِ ارداکنج   karyâhâ-ye ardâkonjFr.: fonctions orthogonales   A set of functions, any two of which, by analogy to orthogonal vectors, vanish if their product is summed by integration over a specified interval.→ orthogonal; → function. orthogonal lines   خط‌هایِ ارداکنج   xatthâ-ye ardâkonjFr.: droites orthogonales   Perpendicular lines.→ orthogonal; → line. orthogonal trajectory   ترایشانه‌ی ِ ارداکنج   tarâyešâne-ye ardâkonjFr.: trajectoire orthogonale   Math.: An → isogonal trajectory where the family of curves are cut at right angles.→ orthogonal; → trajectory. orthogonal vectors   بردارهای ِ ارداکنج   bordârhâ-ye ardâkonjFr.: vecteurs orthogonaux   Two non-zero vectors which are perpendicular, i.e. their → scalar product is zero.→ orthogonal; → vector. orthogonality   ارداکنجی   ardâkonjiFr.: orthogonalité   1) The property of → orthogonal functions. 2) The following conditions satisfied by the → Fourier series: ∫ cos (mx) sin (nx) dx = 0 (summed from -π to +π) for all m, n∫ cos (mx) cos (nx) dx = 0 (summed from -π to +π) for all m ≠ n, = 2π for m = n = 0, = π for (m = n) > 0 ∫ sin (mx) sin (nx) dx = 0 (summed from -π to +π) for m ≠ n, = π for (m = n) > 0.→ orthogonal; → -ity.